English
Convolution of two real Gaussians results in a Gaussian with parameter sums.
Русский
Свертка гауссианов даёт гауссиан с суммой параметров.
LaTeX
$$$ (\mathcal{N}(m_1,v_1) * \mathcal{N}(m_2,v_2)) = \mathcal{N}(m_1+m_2, v_1+v_2). $$$
Lean4
/-- Geometric distribution with success probability `p`. -/
noncomputable def geometricPMF (hp_pos : 0 < p) (hp_le_one : p ≤ 1) : PMF ℕ :=
⟨fun n ↦ ENNReal.ofReal (geometricPMFReal p n),
by
apply ENNReal.hasSum_coe.mpr
rw [← toNNReal_one]
exact (geometricPMFRealSum hp_pos hp_le_one).toNNReal (fun n ↦ geometricPMFReal_nonneg hp_pos hp_le_one)⟩